| Title:
|
Borel matrix (English) |
| Author:
|
Weber, Michel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
401-415 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the Borel summation method. We obtain a general sufficient condition for a given matrix $A$ to have the Borel property. We deduce as corollaries, earlier results obtained by G. M"uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the $L^p$-setting, we establish necessary conditions of the same kind by using Bourgain's entropy criterion. (English) |
| Keyword:
|
Borel matrix |
| Keyword:
|
almost sure convergence |
| Keyword:
|
\text{\sl GB} and \text{\sl GC} sets |
| Keyword:
|
Gaussian processes |
| MSC:
|
28D05 |
| MSC:
|
40G10 |
| MSC:
|
49A35 |
| MSC:
|
60F15 |
| MSC:
|
60G15 |
| idZBL:
|
Zbl 0837.28014 |
| idMR:
|
MR1357539 |
| . |
| Date available:
|
2009-01-08T18:18:48Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118766 |
| . |
| Reference:
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| Reference:
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[W3] Weber M.: GC sets, Stein's elements and matrix summation methods.Prépublication IRMA no 027, Université de Strasbourg, 1993. |
| Reference:
|
[W4] Weber M.: GB and GC sets in ergodic theory.IXth Conference on Probability in Banach Spaces, Sandberg, August 1993, Denmark, Progress in Prob. V, Birkhauser, t. 35, 1994. Zbl 0808.28011, MR 1308514 |
| Reference:
|
[W5] Weber M.: Coupling of the GB set property for ergodic averages.to appear in J. Theoretic. Prob. (1995), 1993. Zbl 0851.60037, MR 1371072 |
| . |
